Time series of financial asset values exhibit well-known statistical features such as heavy tails and volatility clustering. We propose a nonparametric extension of the classical Peaks-Over-Threshold method from extreme value theory to fit the time varying volatility in situations where the...

Intraday Value-at-Risk (VaR) is one of the risk measures used by market participants involved in high-frequency trading. High-frequency log-returns feature important kurtosis (fat tails) and volatility clustering (extreme log-returns appear in clusters) that VaR models should take into account....

We describe smooth non-stationary generalized additive modelling for sample extremes, in which spline smoothers are incorporated into models for exceedances over high thresholds. Fitting is by maximum penalized likelihood estimation, with uncertainty assessed by using differences of deviances...

We consider the modelling of extreme returns in financial time series, and introduce a marked point process model for the exceedances of a high threshold. This model has a self-exciting, Hawkes-process structure in which recent events affect the current intensity of threshold exceedances more...